Risk-averse Decision Research Articles

Information Gap Decision Theory-Based Risk-Constrained Bidding Strategy of Price-Taker GenCo in Joint Energy and Reserve Markets

This paper presents an optimal bidding strategy for price-taker generation companies (GenCos), which participate in a day-ahead joint energy and reserve market. Moreover, this problem is formulated as a Mixed-Integer Quadratic Constrained Program (MIQCP) to maximize the profit. Also, the price uncertainties of energy and reserve markets prices have direct impacts on the expected profit and bidding curves. This optimization problem is modeled with utilization of information gap decision theory (IGDT) for optimizing robustness to failure—or opportunity to windfall—under uncertainty conditions. IGDT assesses the robustness/opportunity of bidding strategy in the face of price uncertainties to determine whether a decision is risk-averse or risk-taking. Correlations among the prices of energy and reserve markets are properly modeled based on the concept of weighted average squared error using a variance–covariance matrix. It is shown that the risk-averse decisions, as well as risk-taking decisions, will affect both expected profit and bidding curves. The proposed method is verified in simulation studies on a GenCo comprising 5-unit thermal that participates in a day-ahead joint energy and reserve markets. Also, the proposed model is applied to a 54-unit thermal GenCo of IEEE-118 bus to validate the computational effectiveness of the proposed model in large system.

Designing Graphs to Communicate Risks: Understanding How the Choice of Graphical Format Influences Decision Making.

Previous research suggests that the choice of graphical format for communicating risk information affects both understanding of the risk magnitude and the likelihood of acting to decrease risk. However, the mechanisms through which these effects work are poorly understood. To explore these mechanisms using a real-world scenario, we examined the relative impact of two graphical displays for depicting the risk of exposure to unexploded ammunition during potential land redevelopment. One display depicted only the foreground information graphically (a bar graph of the number of people harmed), and a second depicted the foreground and background graphically (a stacked bar graph representing both the number harmed and at risk). We presented 296 participants with either the foreground-only or the foreground and background graphical display and measured a broad set of outcome variables, examining (1) the graphical display effect on each of the outcome measures and (2) the pathways by which any display effects work to influence decision making. We found that the foreground-only graphical display increased perceived likelihood and experienced fear, which produced greater worry, which in turn increased risk aversion. In addition, a positive evaluation of the communication materials increased support for policies related to land redevelopment, whether those policies were risk taking or risk mitigating. Finally, the foreground-only graphical display decreased understanding of the risk magnitude, showing that approaches to accomplish one risk communication goal (promoting risk-averse decisions) may do so at the expense of another goal (increasing understanding).

Risk Averse Decision Models for Resilient Supplier Selection

Decision models provided by this study aim to help managers to find remedies to devastating supply chain disruptions that could be caused by a mismatch between volatile customer demand and unreliable supply. We considered the newsvendor problem where the firm has more than one suppliers who are not necessarily reliable. We have provided a range of decision models with risk neutral and risk averse objective functions. The model uses scenarios to represent uncertain events (specifying customer demand and supplier reliability). Linear Programming formulations are provided which can be easily solved using commercially available software. A sample numerical study is also carried out to provide valuable managerial insights for optimal sourcing behaviors of risk averse and risk neutral firms. In the numerical study, expected profit, CVaR and Mean Excess Regret models are selected for evaluation.

Design of a risk-averse decision making tool for smart distribution network operators under severe uncertainties: An IGDT-inspired augment ε-constraint based multi-objective approach

In the context of restructured electricity market and smart grid, uncertainties including renewable generation, load demand, and electricity price would significantly affect the technical and financial aspects of smart distribution networks. This paper presents a risk-averse decision making tool to help distribution network operator (DNO) in short-term operational activities. The objective is to optimize hourly sale prices offered to the customers, transactions (purchase/sale) with the wholesale market, commitment of distributed generation, dispatch of energy storage systems, and planning of interruptible loads in a way that a target profit for the risk-averse DNO is guaranteed. A bi-level information gap decision theory (IGDT) inspired problem is developed to hedge the DNO against risk imposed by the information gap between the forecasted and actual uncertain variables. The bi-level problem is recast into its equivalent single level problem driven by Karush-Kuhn-Tucker optimality conditions. Since the uncertain variables compete with each other to maximize their enveloped-bounds, the augmented ε-constraint method is used to solve the proposed IGDT-inspired multi-objective optimization problem. A Monte Carlo simulation based after-the-fact analysis is conducted to verify the robust performance of the operational decisions. The effectiveness and efficiency of the proposed model are evaluated on the 33-bus and the 118-bus modified test networks.

Nonparametric adaptive Bayesian regression using priors with tractable normalizing constants and under qualitative assumptions

Shape constrained regression models are useful for analyzing data with specific shape responses, such as (monotone) dose-response curves, the (concave) utility functions of a risk averse decision maker, the (increasing) growth curves of children's height through time, that are particularly common in medicine, economic and epidemiological studies. This paper proposes a new adaptive Bayesian approach towards constructing prior distributions, with known normalizing constants, which enables us to take into account combinations of shape constraints and to localize each shape constraint on a given interval. Our strategy enables us to compute the simulation from the posterior distribution using a reversible jump Metropolis–Hastings scheme. The major advantages of the proposal are its flexibility achieved by adjusting local shape restrictions to detect better the high and low variability regions of the data and to facilitate the control of the regression function shape when there is no data at all in some regions. We give asymptotic results that show that our Bayesian method provides consistent function estimator from the adaptive prior. The performance of our method is investigated through a simulation study with small samples. An analysis of two real data sets is presented to illustrate the new approach.

Are Risk Preferences Time-Dependent? Looking Ahead, a Group Has a Stronger Effect Than the Average of Its Individual Members

We investigate whether individual and group risk preferences are dependent on reward delay. To do so, we run a lottery-choice experiment, where payments are made either directly or in 3, 9, or 18 months after the experiment. We find that risk preference is time-dependent for both individuals and groups. In the present, groups make more risk-averse decisions than individuals do. As soon as decisions materialize in the future, this relation reverses, with groups becoming less risk-averse in their decisions and reaching almost risk neutrality at 18 months. Both, individuals and groups, do not significantly differ in their risk preferences between the different delays. We present a parameterization of the probability time trade-off model extended by the probability of prospect survival and show that our results are consistent with the affect-based reasoning explanation.

Strategic multiyear transmission expansion planning under severe uncertainties by a combination of melody search algorithm and Powell heuristic method

In this paper, a new strategic multiyear model is presented for Transmission Expansion Planning (TEP) in deregulated environments. This methodology is based on a tri-level decision making whose fundamental elements are pool-based electricity market and strategic behavior of market participants. In addition, to minimize risks of planning arising from severe uncertainties, an information gap decision theory (IGDT) is used. By using the IGDT, the TEP model is formulated for the risk-averse and risk-seeker decision makers through the robustness and opportunity models, respectively. The offered model is formulated as a non-convex mixed-integer non-linear optimization problem. With this regards, a combination of melody search algorithm and improved Powell heuristic method is widely used to determine the optimal solution. The planning methodology has been applied to the IEEE 30-bus test system and to the large-scale Iranian 400-kV transmission grid. Simulation results demonstrate the feasibility and effectiveness of the proposed model, and the fact that it can be profitable for the real-world networks.

A Stochastic Framework for Multi-stage Generation Expansion Planning under Environmental and Techno-economic Constraints

In this article, a new stochastic framework is proposed for multi-stage generation expansion planning subject to environmental/techno-economic constraints. In this framework, with a new point of view, impacts of expansion plans on strategic behaviors of both generation companies and distribution companies are evaluated. To do so, the proposed framework is developed as a three-level model. The lower level indicates a pool-based electricity market, the intermediate level provides strategic interactions among all market participants, and the upper level represents the generation expansion planning by considering the outcomes of the previous levels. To minimize risks of planning arising from severe uncertainties, a well-founded information gap decision theory is used to model both risk-averse and risk-taker decision makers. The newly developed model is a non-convex non-linear mixed-integer optimization problem. A new melody search algorithm and an innovative augmented Powell heuristic method are employed to obtain the final optimal solution. The feasibility and capabilities of the proposed methodology are illustrated on the 46-bus south Brazilian electric power grid. The obtained results from case studies validate the profitability of the newly developed framework.

Benefit and Risk Balance Optimization for Stochastic Hydropower Scheduling

Limited by inflow forecasting methods, the forecasting results are so unreliable that we have to take their uncertainty and risk into account when incorporating stochastic inflow into reservoir operation. Especially in the electricity market, punishment often happens when the hydropower station does not perform as planned. Therefore, focusing on the risk of power generation, a benefit and risk balance optimization model (BRM) which takes stochastic inflow as the major risk factor is proposed for stochastic hydropower scheduling. The mean-variance theory is firstly introduced into the optimal dispatching of hydropower station, and a variational risk coefficient is employed to give service to managers’ subjective preferences. Then, the multi-period stochastic inflow is simulated by multi-layer scenario tree. Moreover, a specific scenario reduction and reconstruction method is put forward to reduce branches and computing time accordingly. Finally, the proposed model is applied to the Three Gorges Reservoir (TGR) in China for constructing a weekly generation scheduling in falling stage. Compared to deterministic dynamic programming (DDP) and stochastic dynamic programming (SDP), BRM achieves more satisfactory performance. Moreover, the tradeoffs for risk-averse decision makers are discussed, and an efficient curve about benefit and risk is formed to help make decision.

To trust or not to trust: social decision-making in post-institutionalized, internationally adopted youth.

Chronic parental maltreatment has been associated with lower levels of interpersonal trust, and depriving environments have been shown to predict short-sighted, risk-averse decision-making. The present study examined whether a circumscribed period of adverse care occurring only early in life was associated with biases in trust behavior. Fifty-three post-institutionalized (PI) youth, adopted internationally on average by 1year of age, and 33 never-institutionalized, non-adopted youth (Mage =12.9years) played a trust game. Participants decided whether or not to share coins with a different anonymous peer in each trial with the potential to receive a larger number of coins in return. Trials were presented in blocks that varied in the degree to which the peers behaved in a trustworthy (reciprocal) or untrustworthy (non-reciprocal) manner. A comparison condition consisted of a computerized lottery with the same choices and probabilistic risk as the peer trials. Non-adopted comparison youth showed a tendency to share more with peers than to invest in the lottery and tended to maintain their level of sharing across trials despite experiencing trials in which peers failed to reciprocate. In contrast, PI children, particularly those who were adopted over 1year of age, shared less with peers than they invested in the lottery and quickly adapted their sharing behavior to peers' responses. These results suggest that PI youth were more mistrusting, more sensitive to both defection and reciprocation, and potentially more accurate in their trusting decisions than comparison youth. Results support the presence of a sensitive period for the development of trust in others, whereby conditions early in life may set long-term biases in decision-making.

Ambiguity in risk preferences in robust stochastic optimization

We consider robust stochastic optimization problems for risk-averse decision makers, where there is ambiguity about both the decision maker’s risk preferences and the underlying probability distribution. We propose and analyze a robust optimization problem that accounts for both types of ambiguity. First, we derive a duality theory for this problem class and identify random utility functions as the Lagrange multipliers. Second, we turn to the computational aspects of this problem. We show how to evaluate our robust optimization problem exactly in some special cases, and then we consider some tractable relaxations for the general case. Finally, we apply our model to both the newsvendor and portfolio optimization problems and discuss its implications.

Decision Support for IT Investment Projects

Managerial flexibilities have to be taken into account in ex-ante decision-making on IT investment projects (ITIPs). In many papers of the IS literature, standard financial option pricing models are used to value such managerial flexibilities. Based on a review of the related literature, the paper critically discusses the assumptions of the most frequently used financial option pricing model, namely the Black–Scholes model, arguing for relaxed assumptions that better represent the characteristics of ITIPs. The authors find that existing real option analysis approaches featured in the IS, Finance, and Economics literature are unable to consider more than two of our relaxed assumptions. Consequently, they present their own approach in form of a simulation model for the valuation of real options in ITIPs which offers a better representation of the characteristics of ITIPs by taking the discounted cash-flows and the runtime to be uncertain as well as the market to be incomplete. Based on these modifications of the Black–Scholes model’s assumptions, it is found that the resulting option value contains idiosyncratic risk that has to be taken into account in ITIP decision making. For the realistic case of risk averse decision makers, the consideration of idiosyncratic risk usually leads to a lower risk-adjusted option value, compared to one calculated by means of the Black–Scholes model. This confirms the perception of managers who feel that financial option pricing models frequently overvalue ITIPs and hence may induce flawed investment decisions.

Risk minimising strategies for revenue management problems with target values

Consider a risk-averse decision maker in the setting of a single-leg dynamic revenue management problem with revenue controlled by limiting capacity for a fixed set of prices. Instead of focussing on maximising the expected revenue, the decision maker has the main objective of minimising the risk of failing to achieve a given target revenue. Interpreting the revenue management problem in the framework of finite Markov decision processes, we augment the state space of the risk-neutral problem definition and change the objective function to the probability of failing a certain specified target revenue. This enables us to obtain a dynamic programming solution that generates the policy minimising the risk of not attaining this target revenue. We compare this solution with recently proposed risk-sensitive policies in a numerical study and discuss advantages and limitations.

Tradeoffs for Downside Risk-Averse Decision-Makers and the Self-Protection Decision

In addition to risk aversion, decision-makers tend to be also downside risk averse. Besides the usual size for risk trade-off, this allows several other trade-offs to be considered. The decision to increase the level of self-protection generates five trade-offs each involving an unfavourable downside risk increase and an accompanying beneficial change. Five stochastic orders that correspond to these trade-offs are defined, characterised and used to prove comparative static theorems that provide information concerning the self-protection decision. The five stochastic orders are general in nature and can be applied in any decision model where downside risk aversion is assumed.

A Theory of Rational Demand for Index Insurance

Rational demand for index insurance products is shown to be fundamentally different to that for indemnity insurance products due to the presence of basis risk. In particular, optimal demand is zero for infinitely risk-averse individuals, and is nonmonotonic in risk aversion, wealth, and price. For a given belief, upper bounds are derived for the optimal demand from risk-averse and decreasing absolute risk-averse decision makers. A simple ratio for monitoring basis risk is presented and applied to explain the low level of demand for consumer hedging instruments as a rational response to deadweight costs and basis risk. (JEL D14, D81, G13, G22, Q14)

A Dynamic Real Option-Based Investment Model for Renewable Energy Portfolios

This work proposes a dynamic model to devise the optimal risk-averse investment policy in a portfolio of complementary renewable sources for a generation company in the Brazilian power system. The proposed method merges a static energy-contracting model, based on a hybrid robust-and-stochastic optimization approach, with a mean reverting binomial lattice model for real-option valuation. The proposed merge extends previous works by providing support to risk-averse investment decisions in complementary renewable sources dynamically distributed over time. The most important results of the model are: how much capacity to invest or build from each renewable source, how much to sell from the energy portfolio in bilateral contracts, and the optimal timing to invest. Unlike previous reported works, our model takes into account three classes of uncertainties simultaneously: renewable production of candidate sources and prices in the spot and contract markets. A case study with realistic data from the Brazilian power system is presented to illustrate the value of our model.

Wildfires: Systemic changes required

In their Policy Forum “Reform forest fire management” (18 September, p. [1280][1]), M. P. North et al. highlight public support and improved spatial planning as key leverage points to deemphasize fire exclusion and expand beneficial fire. Although these steps are necessary, we caution that they are insufficient to overcome barriers to change. There needs to be a deeper, systems-level understanding of the fire management system. The behavior of fire managers is a direct and logical result of the structure of the system in which they operate, influenced by factors such as incentives, culture, and capacity. If managers are judged by fire exclusion, that will become the dominant paradigm. Managers within this system may operate at cross-purposes, as shown by the widely divergent fire management policies and objectives across jurisdictional boundaries ([ 1 ][2], [ 2 ][3]). The joint influences of complexity, conflict, and uncertainty lead to a risk-averse decision structure constrained by perceptions and pressures, and susceptible to suboptimal decision biases and solutions to problems. The emphasis on aggressive suppression over less tangible ecological benefits and hazard mitigation disconnects fire management objectives from underlying resource management objectives. Infusing risk management principles into fire management decisions would directly address these systemic issues. We propose that efforts targeting transformation focus on four areas: (i) Engage in multiparty risk communication and prioritization of investments based on who can most efficiently mitigate risks. (ii) Track how, why, and with what information decisions are made, and ensure that decision processes are relevant and responsive to organizational and stakeholder needs. (iii) Invest in research to improve knowledge of fire management effectiveness, and consistently integrate new information. (iv) Cultivate a workforce well versed in risk management and the means to integrate this knowledge into decision-making. Transforming fire management is not an inevitable consequence of enhanced support or planning alone; it requires meaningful organizational change in how and why fire response is determined. Adopting systems and risk analysis principles to better understand and improve fire management decisions is a critical step toward effecting comprehensive change. 1. [↵][4]1. D. Calkin, 2. M. P. Thompson, 3. A. A. Ager, 4. M. Finney , For. Pol. Econ. 13, 378 (2011). [OpenUrl][5][CrossRef][6][PubMed][7][Web of Science][8] 2. [↵][9]National Cohesive Wildland Fire Management Strategy ([www.forestsandrangelands.gov/strategy/index.shtml][10]). [1]: /lookup/doi/10.1126/science.aab2356 [2]: #ref-1 [3]: #ref-2 [4]: #xref-ref-1-1 View reference 1 in text [5]: {openurl}?query=rft.jtitle%253DTrends%2Bin%2BEcology%2B%2526%2BEvolution%26rft.stitle%253DTrends%2Bin%2BEcology%2B%2526%2BEvolution%26rft.aulast%253DBond%26rft.auinit1%253DW.%2BJ.%26rft.volume%253D20%26rft.issue%253D7%26rft.spage%253D387%26rft.epage%253D394%26rft.atitle%253DFire%2Bas%2Ba%2Bglobal%2B%2527herbivore%2527%253A%2Bthe%2Becology%2Band%2Bevolution%2Bof%2Bflammable%2Becosystems.%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.tree.2005.04.025%26rft_id%253Dinfo%253Apmid%252F16701401%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [6]: /lookup/external-ref?access_num=10.1016/j.tree.2005.04.025&link_type=DOI [7]: /lookup/external-ref?access_num=16701401&link_type=MED&atom=%2Fsci%2F350%2F6263%2F920.2.atom [8]: /lookup/external-ref?access_num=000230504500010&link_type=ISI [9]: #xref-ref-2-1 View reference 2 in text [10]: http://www.forestsandrangelands.gov/strategy/index.shtml

Exponential utility functions aid upstream decision making

Although the concepts and mathematics of utility theory and its application to adjusting valuations to reflect the perspectives of decision makers with a range of risk preferences have been established for decades, these concepts and numerical applications remain relatively rarely applied by decision makers in the upstream gas and oil industries. Utility functions are now extensively used to assist evaluation of oil and gas hedging and trading of financial and physical commodities from the risk preferences of the parties involved. This study makes the case for more extensive use of utility functions in the upstream gas and oil sectors by presenting cases that highlight both the conceptual and valuation benefits that result from their application.Exponential utility functions adequately describe the risk preferences of risk-averse and risk-prone decision makers for a wide range of upstream gas and oil asset types and circumstances. Simple equations for the calculation of utility factors and expected utility factors, i.e., taking into account probabilities of a range of outcomes being realised, are presented and compared with the equivalent linear utility functions of a risk-neutral investor valuing assets based on unrisked discounted cash flow (i.e. net present value, NPV) and risked discounted cash flow (i.e., expected monetary value, EMV). The additional insight gained from applying utility functions is considered with examples for high-uncertainty exploration assets, decision makers constrained by various loss tolerances and selection of optimum gas field development plans from a number of distinct alternative plans. In all cases considered the utility functions provide decision makers with greater insight than just the consideration of NPV and/or EMV. A case is therefore made to justify more extensive use of utility functions by upstream decision makers.

Non-probabilistic Decision Strategies Behind the Veil

In his writings on justice, John Rawls notably introduced an initial testing procedure he dubbed the original position. It describes a hypothetical situation in which several rational, self-interested agents are placed behind a so called veil of ignorance and asked to make a definitive decision on what type of society they would live in. Rawls argues that the rational agents in the original position would choose according to a maximin decision strategy; that is, they would choose to maximize the worst possible payoff. He backs this by arguing that the situation itself drives the agents to act as risk-averse decision makers, as this is no regular everyday decision, but one which will affect all of their future life and all their future decisions. Notably, contra Rawls, John Harsanyi argues that, while some degree of riskaversion within the original position is rationally sustainable by the uniqueness of the situation and the weight of the decision, Rawlsian agents are characterized by an extreme, highly irrational risk-aversion in choosing the maximin strategy. That is

Optimal Information Blending with Measurements in the L2 Sphere

A sequential information collection problem, where a risk-averse decision maker updates a Bayesian belief about the unknown objective function of a linear program, is used to investigate the informational value of measurements performed to refine a robust optimization model. The information is collected in the form of a linear combination of the objective coefficients, subject to random noise. We have the ability to choose the weights in the linear combination, creating a new, nonconvex continuous-optimization problem, which we refer to as information blending. We develop two optimal blending strategies: (1) an active learning method that maximizes uncertainty reduction and (2) an economic approach that maximizes an expected improvement criterion. Semidefinite programming relaxations are used to create efficient convex approximations to the nonconvex blending problem.